which deviation regulates the lqr exactly

i have a running simulation in which i want to use an lqr controller, did i understand correctly? that the lqr brings the deviation from zero in the initial conditions back to zero, and in that case should I enter the initial conditions as parameters that are updated during the simulation?

my second question is: the system matrix A is dependent on other parameters (speed) in the simulation so that it is constantly changing, will then in each step during the simulation the Lqr calculate new A matrix and therefore output new K values? is that possible?

Answer 1

[Prathamesh]

Hi,

I understand that you want to know how “lqr” algorithm works and how is K matrix computed when A is a variable matrix.

LQR basically decreases the sum of square of errors between the actual state and desired state.

Initial condition is basically initial state of the system. You can input it based on your system.

Refer to the documentation of LQR for more information about this.

https://in.mathworks.com/help/control/ref/lti.lqr.html

Now if A and B are state dependent or variable matrices then the lqr algorithm solves state dependent Riccati equation (SDRE)

LMI is a better tool solve these equations, refer to the documentation below.

https://in.mathworks.com/help/robust/lmis.html

Also, refer to this paper to get more information on this topic.

https://dcsl.gatech.edu/papers/aiaa10a.pdf